\newproblem{lay:1_4_32}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 1.4.32}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Carlos Oscar Sorzano, Aug. 31st, 2013} \\}{}

  % Problem statement
	Could a set of 3 vectors in $\mathbb{R}^4$ span all of $\mathbb{R}^4$? Explain. What about $n$ vectors in $\mathbb{R}^m$ when $n$ is less than $m$?
}
{
  % Solution
	None of the two situations is possible. To span all $\mathbb{R}^4$ one need at least 4 vectors (in fact it is enough with 4 linearly independent vectors).
	The same happens with $\mathbb{R}^m$, one needs at least $m$ vectors. Any smaller number of vectors cannot fully span $\mathbb{R}^m$.
}
\useproblem{lay:1_4_32}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}
